Ramsey numbers for local colorings
A coloring of the edges of a graph is a local k-coloring if no more than k colors are used in coloring the edges containing any vertex. The local k-Ramsey number of a graph G, \(r^ k_{loc}(G)\), is the minimum integer M so that given any local k-coloring of the complete graph on M vertices then there exists a monochromatic copy of G. The authors prove that \(r^ k_{loc}(G)\) is always well defined, compute the exact value of \(r^ k_{loc}(G)\) for several special graphs G, and prove several relationships between the local Ramsey numbers and the Ramsey numbers as they are usually defined.
scientific article; zbMATH DE number 4006298